Monte Carlo Hauser-Feshbach predictions of prompt fission $\gamma$ rays: Application to $n_{\mathrm{th}}+{}^{235}$U, $n_{\mathrm{th}}+{}^{239}$Pu, and ${}^{252}$Cf (sf)

The prompt neutron and $\gamma$ emission from primary fission fragments are calculated for thermal neutron induced fission of ${}^{235}$U and ${}^{239}$Pu and for spontaneous fission of ${}^{252}$Cf using a Monte Carlo Hauser-Feshbach approach for the evaporation of the excited fission fragments. Remaining free model parameters, such as excitation energy sharing and initial spin distribution, are determined by comparison of the neutron emission characteristics with experimental data. Using the obtained parameters the $\gamma$-ray characteristics, e.g., $\gamma$ spectrum, multiplicity distribution, average multiplicity and energy, and multiplicity distribution, are calculated and compared with available experimental data.

Figure 1

Primary fission fragment yields as a function of mass and total kinetic energy for $n_{\mathrm{th}}+{}^{235}$U, as measured by Romano et al. [16]. The units of the color scale are in percent. The yield is normalized to 200$\%$.

Figure 2

Same as Fig. 1 but for $n_{\mathrm{th}}+{}^{239}$Pu. The units of the color scale are in percent. The yield is normalized to 200$\%$. Contrary to Fig. 1, this plot was obtained by computing the yields directly from Eq. (8).

Figure 3

${\overline{\nu }}_l/{\overline{\nu }}_h$ as a function of the heavy fragment mass using $R_T=1.2$ and $R_T\left(A\right)$. $R_T\left(A\right)$ was obtained by minimizing the discrepancies of the calculated ratio and of the experimental data of Nishio et al. [23] and Vorobyev et al. [24].

Figure 4

Neutron emission probability ${\Gamma }_n/({\Gamma }_n+{\Gamma }_{\gamma })$ as a function of the excitation energy for different spin values for ${}^{146}$Ba.

Figure 5

Average initial fission fragment spin for $n_{\mathrm{th}}+{}^{235}$U as a function of the fragment mass for MCHF calculations using a constant spin cutoff parameter $B=12\hslash$, using a temperature, mass and ground state deformation dependent spin cutoff parameter and using a saw-tooth like spin cutoff parameter $B$($A$). Experimental values are taken from Durell (digitized from Ref. [25]), Naik et al. [29] and Aumann et al. [28].

Figure 6

Average prompt fission neutron multiplicity (PFNM) for $n_{\mathrm{th}}+{}^{235}$U as a function of the fragment mass: (a) A constant value $R_T=1.0$ as well as a the mass-dependent $R_T\left(A\right)$ parameter was used for the Monte Carlo Weisskopf Spectrum (MCW) calculations. (b) The Monte Carlo Hauser Feshbach (MCHF) calculation is obtained using a mass-dependent $R_T\left(A\right)$ parameter and a temperature, mass and ground state deformation dependent spin cutoff parameter $B$. Experimental values are taken from Nishio et al. [23], Maslin et al. [34], Batenkov et al. [35], and Vorobyev et al. [24].

Figure 7

Neutron multiplicity distributions for $n_{\mathrm{th}}+{}^{235}$U obtained in Monte Carlo Weisskopf spectrum (MCW) and Monte Carlo Hauser-Feshbach (MCHF) calculations vs. the experimental data of Franklyn et al. [36], Boldeman et al. [37], Diven et al. [38], and Holden et al. [39].

Figure 8

Average prompt fission neutron spectrum for $n_{\mathrm{th}}+{}^{235}$U in ratio to a Maxwellian with temperature $T=1.35$ MeV. Those results were calculated based on a Weisskopf (MCW) and Hauser-Feshbach (MCHF) models using $R_T\left(A\right)$ and $B(T,A,\beta )$. Results are compared to the ENDF/B-VII.0 evaluation [33], as well as experimental data by Kornilov et al. [40] and Vorobyev et al. [41].

Figure 9

Same as Fig. 8, but plotted on an absolute scale.

Figure 10

Average center-of-mass energy of the prompt fission neutrons for $n_{\mathrm{th}}+{}^{235}$U as a function of the fragment mass. (a) A constant value $R_T=1.0$ as well as a mass-dependent $R_T\left(A\right)$ parameter were used for the Monte Carlo Weisskopf spectrum (MCW) calculations. (b) The Monte Carlo Hauser-Feshbach (MCHF) calculations were obtained using a mass-dependent $R_T\left(A\right)$ parameter and a temperature, mass and ground state deformation dependent spin cutoff parameter $B$. Experimental values are taken from Nishio et al. [23], Batenkov et al. [35], and Vorobyev [41].

Figure 11

Average prompt fission $\gamma$ multiplicity for $n_{\mathrm{th}}+{}^{235}$U as a function of the fragment mass. A constant value spin cut-off parameter $B=12\hslash$ as well as temperature, mass and ground state deformation dependent spin cut-off parameter $B$ was used in the Monte Carlo Hauser Feshbach (MCHF) calculations. Experimental values are taken from Pleasonton et al. [42] and Albinsson et al. [45].

Figure 12

Average $\gamma$ energy for $n_{\mathrm{th}}+{}^{235}$U as a function of the fragment mass. A constant value spin cut-off parameter $B=12\hslash$ as well as temperature, mass and ground state deformation dependent spin cut-off parameter $B$ was used in the Monte Carlo Hauser-Feshbach (MCHF) calculations. Experimental values are taken from Pleasonton et al. [42]. Experimental sample error bars are shown at 5-u intervals.

Figure 13

Monte Carlo Hauser-Feshbach model (MCHF) calculation of the $\gamma$ multiplicity distribution for $n_{\mathrm{th}}+{}^{235}$U vs. the negative binomial model of Valentine [46] (with ${\overline{N}}_{\gamma }$ $=$ 7.93 and $D_{\gamma }=1.07$).

Figure 14

Monte Carlo Hauser-Feshbach model (MCHF) calculation of the prompt fission $\gamma$ spectrum for $n_{\mathrm{th}}+{}^{235}$U vs. experimental data of Verbinski et al. [43] and Maienschein et al. [52] and ENDF/B-VII.0 data [33].

Figure 15

Same as Fig. 14, but plotted in log-log.

Figure 16

Monte Carlo Hauser-Feshbach model (MCHF) calculations of of the average prompt fission neutron multiplicity for $n_{\mathrm{th}}+{}^{239}$Pu as a function of the fragment mass. Experimental values are taken from Batenkov [35], Apalin [53], Nishio [23], and Tsuchiya [54].

Figure 17

Monte Carlo Hauser-Feshbach model (MCHF) calculations of the average center-of-mass energy of the prompt fission neutrons vs. experimental values of Batenkov [35] and Tsuchiya [54] for $n_{\mathrm{th}}+{}^{239}$Pu.

Figure 18

Monte Carlo Hauser-Feshbach model (MCHF) calculations of the neutron multiplicity distribution for $n_{\mathrm{th}}+{}^{239}$Pu compared to the evaluation based on experimental data of Holden and Zucker [39].

Figure 19

Monte Carlo Hauser-Feshbach model (MCHF) calculation of the average prompt fission neutron spectrum for $n_{\mathrm{th}}+{}^{239}$Pu in ratio to a Maxwellian with temperature $T=1.42$ MeV. Results are compared to the ENDF/B-VII.0 evaluation [33], as well as experimental data by Bojcov [55], Starostov [56], and Knitter [57].

Figure 20

Average prompt fission $\gamma$ multiplicity for $n_{\mathrm{th}}+{}^{239}$Pu as a function of the fragment mass. Results of the Monte Carlo Hauser-Feshbach (MCHF) calculations are compared to experimental values from Pleasonton [58].

Figure 21

Average prompt fission $\gamma$ energy for $n_{\mathrm{th}}+{}^{239}$Pu as a function of the heavy fragment mass. Results of the Monte Carlo Hauser-Feshbach (MCHF) calculations are compared to experimental values from Pleasonton [58].

Figure 22

Monte Carlo Hauser-Feshbach model (MCHF) calculation of the prompt fission $\gamma$ spectrum for $n_{\mathrm{th}}+{}^{239}$Pu compared to experimental data of Verbinski et al. [43] and to the ENDF/B-VII.0 evaluation [33].

Figure 23

Monte Carlo Hauser-Feshbach model (MCHF) calculations of the average prompt fission neutron multiplicity for ${}^{252}$Cf (sf) as a function of the fragment mass. Experimental values are taken from Vorobyev et al. [59] and Bowman et al. [61].

Figure 24

Monte Carlo Hauser-Feshbach model (MCHF) calculations of the average center-of-mass energy of the prompt fission neutrons for ${}^{252}$Cf (sf). Experimental data are taken from Bowman et al. [61], Gavron et al. [62], and Budtz-Jorgensen et al. [63].

Figure 25

Monte Carlo Hauser-Feshbach model (MCHF) calculations of the average prompt fission neutron spectrum for ${}^{252}$Cf (sf) in ratio to a Maxwellian with temperature $T=1.42$ MeV. The calculation are compared to the standard evaluation of Mannhart [64] used by ENDF/B-VII.0 [33] and experimental data from Starostov et al. [65] and Knitter et al. [66].

Figure 26

Monte Carlo Hauser-Feshbach model (MCHF) calculation of the average prompt fission $\gamma$ spectrum for ${}^{252}$Cf (sf) compared to experimental data of Verbinski et al. [43] and to ENDF/B-VII.0 data [33].

Figure 27

Average prompt fission $\gamma$ multiplicity for ${}^{252}$Cf (sf) as a function of the fragment mass. Results of the Monte Carlo Hauser-Feshbach (MCHF) calculations are compared to experimental values from Johansson [70] and MPI [71] and from Pleasonton et al. [67].

Figure 28

Monte Carlo Hauser-Feshbach model (MCHF) calculation of the $\gamma$ multiplicity distribution for ${}^{252}$Cf (sf) compared to experimental data from Brunson [51], Brunson's Model [51], and to the negative binomial model of Valentine [46] (with ${\overline{N}}_{\gamma }$ $=$ 10.5 and $D_{\gamma }=1.074$).